Is there some ‘ideal’ length of time over which a trend should be picked? If so what is it, and what is the justification for choosing it.
This is an excellent question, Latimer. I would say that if you are using a 1 foot ruler to measure things, there is an ideal range of lengths for those things, namely between say 1/16 of an inch and 10 feet. Within that range there is no length that is ideal for measurement by a ruler, the ruler is suitable for all lengths in that range.
By the same token if you are trying to measure the slope of a slightly bumpy incline, there is an ideal range of intervals along that slope to measure it at. It should be longer than a couple of bumps, or the measured slope will be meaningless, but at most the length of the entire incline or errors will enter.
Does that seem reasonable?
Recall that my statement was “If you back off to the bigger picture starting from any time between 1970 and 1990 (so as to be sure there’s no cherry picking going on).” Some people seem to be reading it as “If you back off to the bigger picture starting from 1970.”
My point there was that no matter what starting point you pick, as long as the starting point in a reasonable range, in this case 1970 to 1990, you see the same bumpy slope going up from that point, with no apparent indication of any slowdown in the most recent decade. Starting earlier than 1970 is not reasonable because it’s beyond the length of the incline in question. Later than 1990 is too short because there are not enough bumps to get an idea of the slope.
One you have the slope, you can ask how well the curve in question follows the general pattern of the slope. This seems like a somewhat subjective judgment. For example I would say that the BEST curve follows a general pattern along the whole length of any interval starting between 1970 and 1990 and ending in 2012. But being a subjective judgment, others may well disagree.